1 OBJECTIVE TSW explore polynomial functions through graphing. TODAY’S ASSIGNMENT (due tomorrow) –WS Sec. 3.4 Day 1 REMINDERS –PI Day Celebration:Friday,

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Presentation transcript:

1 OBJECTIVE TSW explore polynomial functions through graphing. TODAY’S ASSIGNMENT (due tomorrow) –WS Sec. 3.4 Day 1 REMINDERS –PI Day Celebration:Friday, 11 March 2016 –PI Day Celebration: Friday, 11 March 2016 You may drop off your pie before school. Do not bring something that needs to be refrigerated! College Algebra K/DC Monday, 29 February 2016

3-2 Polynomial Functions: Graphs, Applications, and Models 3.4 Graphs of f ( x ) = ax n ▪ Graphs of General Polynomial Functions ▪ Turning Points and End Behavior

3-3 Graphing Functions of the Form f ( x ) = ax n ( a = 1) Graph Choose several values for x, and find the corresponding values of f(x), g(x), and h(x).

3-4 Graphing Functions of the Form f ( x ) = ax n ( a = 1) Plot the ordered pairs, and connect the points with a smooth curve.

3-5 Graphing Functions of the Form f ( x ) = ax n ( a = 1) Graph Choose several values for x, and find the corresponding values of f(x), g(x), and h(x).

3-6 Graphing Functions of the Form f ( x ) = ax n ( a = 1) Plot the ordered pairs, and connect the points with a smooth curve.

3-7 Examining Vertical and Horizontal Translations Graph The graph of is the same as the graph of, but translated 1 unit up. It includes the points (–1, 0), (0, 1), and (1, 2).

3-8 Examining Vertical and Horizontal Translations Graph The graph of is the same as the graph of, but translated 2 units right. It includes the points (1, –1), (2, 0), and (3, 1).

3-9 Examining Vertical and Horizontal Translations Graph The graph of is the same as the graph of, but translated 3 units left, reflected across the x-axis, stretched vertically by a factor of ½, and then translated 5 units up. It includes the points (–2, 1.5), (–3, 2), and (–4, 1.5).

3-10 Determining End Behavior Given The Defining Polynomial The end behavior of a polynomial graph is determined by the dominating term (the term of the highest degree), ax n, where a is the leading coefficient and n is the degree of the polynomial. Ex:f(x) = 2x 3 – 8x has the same end behavior as f(x) = 2x 3 (a = 2, n = 3). Ex:f(x) = 2 + 6x – 4x 2 – 3x 4 has the same end behavior as f(x) = –3x 4 (a = –3, n = 4).

3-11 Determining End Behavior Given The Defining Polynomial The four possibilities for end behavior are: anEnd Behavior > 0 even< 0 odd< 0 odd> 0 even

3-12 Determining End Behavior Given The Defining Polynomial Use the symbols for end behavior to describe the end behavior of the graph of each function. Give a reason for your answer. (a) Since a = −1 < 0 and degree = 4 (even), the end behavior is shaped (b)Since a = 1 > 0 and degree = 3 (odd), the end behavior is shaped Two parts to the reason

3-13 Determining End Behavior Given The Defining Polynomial Since a = 1 > 0 and degree = 6 (even), the end behavior is shaped Since a = −1 < 0 and degree = 5 (odd), the end behavior is shaped (c) (d)

3-14 Assignment WS Sec. 3.4: Day 1 –For each graphing problem, draw a table and fill in at least 5 points – at least 2 on either side of the vertex/turning point. –Due on Tuesday, 01 March 2016.